Children\'s Mathematics

Chloë’s older sister, Lydia, was already in the first class in school. A week after the

meeting about schemas, Chloë’s mother sent the note at the opening of this chapter

(see Figure 3.1, p. 37).

Schemas within child-initiated play

One aspect that is significant for the development of schemas is that whilst time and

opportunities for children to explore in their own ways are crucial for schema explo-

ration, certain experiences and materials appear to offer especially rich sources of

exploration.

Painting and drawing, modelling with clay and play-dough, design/technology,

construction materials and block play offered particularly rich opportunities for

schema exploration for the children in this study. When analysed, observations of

play with these resources also had the highest percentage of cognitively challenging

minutes recorded, with art the highest (Worthington, 1996b). Sylva et al. also

found art to be the most challenging experience for children whilst Gura’s study of

block play illustrates its potential for learning (Gura, 1992; Sylva, Roy and Painter,

1980). Like the example of Naomi below, many of the observations with these

resources were of mathematical schemas. It is also interesting to note that the

resources listed above allow children to represent their thinking: this may be

significant for later representation of abstract ideas and symbols, especially in

mathematics.

Intense involvement and challenging learning

Naomi, 4:10, was with a group of children. They had had free access to clay

since entering school, during a long child-initiated play session. Today the nursery

nurse was leading a group who were exploring clay with their hands but without

other tools.

Naomi is rolling a long sausage of clay: several other children have used similar

clay ‘sausages’ to make parts of a person or animal. She joins the ends of her

sausage to form a circle and then rolls some small balls of clay that she places

inside the circle. She stands up for a moment, looks at what she has done and

then places an additional ball on the outer edge of the circle and sits down.Taking

some more clay she twists and moulds it in her hands and breaks the piece in

half, then combines the two pieces. She appears to be oblivious to the busy noise

and movement in the room around her while she rolls another cylinder. At first

the clay in her hands is short and thick but with careful attention it becomes

thinner and longer: it is about 46 centimetres long and of even thickness. Naomi

looks up briefly to see what the other children are doing, then rolls her cylinder

into a ball. Again she transforms the ball of clay into a long cylinder.

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